A good introduction to experimental psi research is Entangled Minds by Dean Radin, a leading parapsychologist, and also his earlier book The Conscious Universe. Another is Parapsychology: The Controversial Science, by Richard Broughton.
Extraordinary Knowing, by Elizabeth Lloyd Mayer, a clinical psychologist, and Outside the Gates of Science by science fiction writer Damien Broderick, are sympathetic personal explorations of the topic. Diane Hennacy Powell's The ESP Enigma is a useful summary by a neuroscientist.
A detailed text book is H.J. Irwin's An Introduction to Parapsychology.
Michael Thalbourne and Lance Storm (eds.), Parapsychology in the Twenty-First Century: Essays on the Future of Psychical Research, is a collection of papers by leading experimenters and theorists.
Statistician Jessica Utts provides an overview of the use of statistics in parapsychology.
Books by J.B. Rhine,for instance New Frontiers of the Mind, cover early ESP research by the founder of modern parapsychology.
M. Ullman and S. Krippner, Dream Studies and Telepathy describes the authors' groundbreaking work into ESP in dreams, the precursor of the later ganzfeld method.
Russell Targ and Harold E. Puthoff, Mind Reach describes the authors' work on remote viewing. Margins of Reality by Robert G. Jahn and Brenda J. Dunne includes chapters on their remote viewing work at Princeton University (see the homepage for Princeton Engineering Anomalies Research (PEAR).
Upton Sinclair's Mental Radio is a classic description of informal experiments he carried out with his wife Craig, convincing him of the reality of telepathic interactions.
Several books have been written about the Stargate (or Star Gate) remote viewing programme carried out on behalf of the US military. A pacy account is Jim Schnabel's Remote Viewers, but see also Jim McMoneagle's, The Stargate Chronicles: Memoirs of a Psychic Spy, by one of the programme's most successful participants. There's also a good chapter on the topic in Broderick's Outside the Gates of Science.
Edwin C. May's article 'The American Institutes for Research Review of the Department of Defense's Star Gate Program: a commentary,' is a robust defence of the programme's value by its director, arguing that a negative assessment by the CIA was driven by political rather than scientific considerations.
See Jessica Utts positive evaluation of Stargate remote viewing data: 'An Assessment of the Evidence for Psychic Functioning'. Ray Hyman's negative evaluation and Utts's response to Hyman can both be found here here.
David Marks's The Psychology of the Psychic contains a robust attack on the remote viewing work by Targ and Puthoff.
Ray Hyman's The Elusive Quarry is a collection of papers describing his engagment with the ganzfeld database and his conclusion that no claims of statistical significance are warranted.
See also James Alcock, Science and Supernature: A Critical Appraisal of Parapyschology. Some of the same ground is covered by James Alcock et al in Psi Wars: Getting to Grips With the Paranormal, which however also includes less sceptical appraisals.
This comments thread contains sceptical arguments about ESP research.
Chris Carter's Parapsychology and the Skeptics is a robust, recent defence of parapsychology exposing the weaknesses in sceptical approaches.
Susan Blackmore is considered to have strengthened the case for psi's non-existence by her repeated failure to find evidence of it in her own experiments. However see this critique of her work by Rick Berger, and her rebuttal.
Rupert Sheldrake has pioneered experimental work, including the sense of being stared at (see his website for links). The Skeptical Inquirer has published a critique of his work on this research, which has also been subjected to scrutiny by critics in The Sense of Being Glared At: see abstract and an editorial introduction.
Not available online, but worth trying to read, are interesting remote reviewing experiments carried out in the 1980s by Marianne Schlitz: see M.J. Schlitz and E. Gruber, 'Transcontinental remote viewing,' Journal of Parapsychology 44, 1980, pp. 305-17; M.J. Schlitz and J. Haight, 'Remote viewing revisited: An intrasubject replication', Journal of Parapsychology 48, 1984, pp. 39-49.
Besides Sheldrake's book on the subject there is a lot of online material relating to the controversy over his work with the dog Jaytee:
Rupert Sheldrake and Pamela Smart, 'A Dog That Seems to Know When His Owner Is Coming Home: Videotaped Experiments and Observations'.
Richard Wiseman's experiments are described here.
Richard Wiseman interview
Skeptico debate between Sheldrake and Wiseman
See also Dean Radin's attempt to correlate the findings to geomagnetism and other local environmental variables and this clip of Sheldrake talking about psychic cats
For a good understanding of psi research there's no substitute for reading the primary research. Look in the archives of the Journal of Scientific Exploration, whose articles can be accessed free. Other main sources are the Journal of the Society for Psychical Research (see the abstracts catalogue here) and the Journal of Parapsychology.